COGENERATOR AND SUBDIRECTLY IRREDUCIBLEIN THE CATEGORY OF S-POSETS
Publish place: Journal of Algebraic Systems، Vol: 2، Issue: 2
Publish Year: 1393
Type: Journal paper
Language: English
View: 660
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Document National Code:
JR_JAS-2-2_005
Index date: 4 August 2015
COGENERATOR AND SUBDIRECTLY IRREDUCIBLEIN THE CATEGORY OF S-POSETS abstract
In this paper we study the notions of cogenerator and subdirectly irreducible in the category of S-posets. First we give some necessary and su cient conditions for an S-poset to be a cogenerator. Then we see that under some conditions, regular in- jectivity implies generator and cogenerator. Recalling Birkho 's Representation Theorem for algebras, we study subdirectly irreducible S-posets and prove this theorem for the category of ordered right acts over an ordered monoid. Among other things, we present the relationship between cogenerators and subdirectly irreducible S-posets.
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COGENERATOR AND SUBDIRECTLY IRREDUCIBLEIN THE CATEGORY OF S-POSETS authors